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Research Papers

Analysis of Locally Nonlinear MDOF Systems Using Nonlinear Output Frequency Response Functions

[+] Author and Article Information
Z. K. Peng

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK; State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, P. R. Chinapengzhike@tsinghua.org.cn

Z. Q. Lang

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKz.lang@shef.ac.uk

S. A. Billings

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKs.billings@shef.ac.uk

J. Vib. Acoust 131(5), 051007 (Sep 11, 2009) (10 pages) doi:10.1115/1.3147139 History: Received October 01, 2008; Revised April 12, 2009; Published September 11, 2009

The analysis of multidegree-of-freedom (MDOF) nonlinear systems is studied using the concept of nonlinear output frequency response functions (NOFRFs), which are a series of one-dimensional functions of frequency recently proposed by the authors to facilitate the analysis of nonlinear systems in the frequency domain. By inspecting the relationships between the NOFRFs of two consecutive masses in the locally nonlinear MDOF systems, a series of properties about the NOFRFs of the nonlinear systems are obtained. These properties clearly reveal how the system linear characteristic parameters govern the distribution of nonlinear effects induced by the system nonlinear component within the whole systems. The results obtained in the present work are of significance to the frequency response analysis for nonlinear systems. One important potential application of these results is the detection and location of damages in engineering structures, which make the structures behave nonlinearly.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 6

The FFT spectra of the system responses obtained using two different inputs ((a) and (c): A=0.2; (b) and (d): A=1.0)

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Figure 5

A 6DOF nonlinear oscillator

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Figure 4

A multidegree-of-freedom nonlinear oscillator

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Figure 3

A multidegree-of-freedom linear oscillator

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Figure 2

The output frequency response of a nonlinear system

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Figure 1

The output frequency response of a linear system

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